Thus, the original spin model is fermionized into bond fermions and gauge fermions that act as local chemical potentials. As long as we are interested in the ground state, the gauge fermions do not play any further role [1]}, [2]}. The eigenstates in the free fermion sector are found by Fourier transformation followed by Bogoliubov transformation [3]}, [4]}. A schematic of the quantum circuit that performs these steps is given in Fig. REF (b) and (c).
